Hi, everybody!

I'm trying get into FM synthesis. As an excercise I decided to recreate some of Yamaha DX7 algoritms in PD and compare results with Korg Volca FM, that is DX7-compatible.

I took FM patch for two operators from FLOSS manual, and extended it to 3 operators stack as shown here:

But resulting sound is much more harsh in comparison with the same patch on Volca. I don't understand what I'm doing wrong.
fm_mod_stack.pd

Thanks for any help in advance!

@roman.galyaminskiy Hi, what you are doing in the patch is "true" frequency modulation, in that you are modulation the frequency of [osc~] objects. Generally the way to do it in software (and indeed how it's done in the DX7, volca etc) is called phase modulation, which is analogous to FM, where instead you modulate the readout phase of cosine oscillators. This approach also allows you to have an oscillator modulating itself (which you need for operator 6 in the algorithm you are trying to emulate), although that needs to happen on a sample-by-sample basis, and you need to use the block~ object inside a subpatch for that.
I fixed your patch to do phase modulation, and now has 6 operators (number 6 has feedback). It probably won't sound exactly like the volca because you are missing a number of features (envelopes, frequency offset, phase locking etc), but it should get you started with exploring FM in Pd, hope it helps.
fm_mod_stack_fix.pd

I attempted to recreate this sort of thing some time ago, with a flexible algorithm structure. It's pretty involved and not intuitive at all, but it's basically the same concept as the above patch. It's a CPU hog enough with only 3 operators, but it sounds pretty good to me.
https://forum.pdpatchrepo.info/topic/10745/3-op-fm-synth-with-mod-matrix

@weightless, thank you so much to your patch! It finally shed some light on this whole FM/PM thing. Sorry, but lots of questions coming:

1. I spent half a day reading about FM/PM, but it's still not clear what's the fuzz is all about. If FM could be described with these equations:
   

And PM with these:

While phase and frequency are connected as following:

(Formulas were take from here: https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part12/page1.html)

Isn't it all the same?

I undersand that perhaps in 80's PM was easier to implement, But if math works essentialy the same in both ways, why do results differ?

2. In my patch I've used modulation index in range 0-14 as it is shown in Chowning's book (as it correspond to 0-99 of operator output for synth):

I notice, that for PM you are using modulation index in range 0-2 (200/100 right?) and it sounds exactly the same? Could you please explain those numbers?

Once again, thank you so much for your help!

@roman.galyaminskiy Unfortunately the math goes way over my head and I cannot explain it to you in those terms. Perhaps someone will come along and be able to do that. Most of what I know about FM/PM comes from the example patch E08.phase.mod.pd, which is pretty much the same as the fixed patch I attached and also the synth I linked is based on that.
The example patch says "good" modulation indexes go from 0 to 1, I used 0 to 2 by ear to be honest.